Remember the fundamental rule: water always goes from areas that are hypotonic to areas that are hypertonic.

In this case, animal cells have no cell wall, so what they want is to simply be at the same concentrations as that of the environment. If the animal cell is in a hypertonic environment, then the cell will lose its water -which is bound to be detrimental. Similarly, if an animal cell is in a hypotonic environment, then it will take in water, and potentially lyse because it has no cell wall.

On the other hand, plant cells have a cell wall, so they like to be in hypotonic environments. This is because the cell wall allows them to take in water and keep the cells turgid, which is exactly how the cell wants to be. If the plant cell were in a hypertonic environment, the water would leave from the cell and the cell would plasmolyze.